In this study, the influences of spatially varying stochastic properties on free vibration analysis of composite plates were investigated via development of a new approach named the deterministic-stochastic Galerkin-based semi-analytical method. The material properties including tensile modulus, shear modulus, and density of the plate were assumed to be spatially varying and uncertain. Gaussian fields with first-order Markov kernels were utilized to define the aforementioned material properties. The stochastic fields were decomposed via application of the Karhunen-Loeve theorem. A first-order shear deformation theory was assumed, following which the displacement field was defined using admissible trigonometric modes to derive the potential and kinetic energies. The stochastic equations of motion of the plate were obtained using the variational principle. The deterministic-stochastic Galerkin-based method was utilized to find the probability space of natural frequencies, and the corresponding mode shapes of the plate were determined using a polynomial chaos approach. The proposed method significantly reduced the size of the mathematical models of the structure, which is very useful for enhancing the computational efficiency of stochastic simulations. The methodology was verified using a stochastic finite element method and the available results in literature. The sensitivity of natural frequencies and corresponding mode shapes due to the uncertainty of material properties was investigated, and the results indicated that the higher-order modes are more sensitive to uncertainty propagation in spatially varying properties.

在这项研究中，通过开发一种基于确定性随机Galerkin的半分析方法，研究了空间变化的随机特性对复合板自由振动分析的影响。包括板的拉伸模量，剪切模量和密度在内的材料特性被假定为空间变化且不确定的。利用具有一阶马尔可夫核的高斯场来定义上述材料属性。随机场通过Karhunen-Loeve定理的应用而分解。假设采用一阶剪切变形理论，然后使用允许的三角模态定义位移场，以导出势能和动能。利用变分原理获得了板的随机运动方程。利用基于确定性-随机Galerkin的方法找到固有频率的概率空间，并使用多项式混沌方法确定板的相应模式形状。所提出的方法大大减小了结构数学模型的大小，这对于提高随机模拟的计算效率非常有用。该方法已使用随机有限元方法进行了验证，并在文献中得到了可用的结果。研究了由于材料性能不确定性引起的固有频率和相应的振型的灵敏度，